Warm a large skillet over medium-high heat and add the olive oil.
Sauté the onion and bell pepper with a pinch of salt until tender and lightly browned, 5–7 minutes. Transfer to a plate.
Melt the butter in the same skillet. Add the sliced steak and cook, stirring, until just browned, 2–3 minutes.
Stir in garlic, Worcestershire, remaining salt, pepper, and smoked paprika. Cook 30 seconds until fragrant.
Return peppers and onions to the pan and toss to combine. Scrape the mixture into a bowl and wipe the skillet clean.
Assemble a quesadilla: place a tortilla in the skillet over medium heat, sprinkle some cheese, add a layer of steak-pepper mixture, then more cheese and a second tortilla.
Cook until the bottom is golden and cheese starts melting, 2–3 minutes. Flip carefully and cook another 2–3 minutes until crisp and melty.
Repeat with remaining tortillas and filling. Rest each quesadilla 1 minute, then slice and garnish with parsley.